In fact I tested to do Dithering too, but I didn't get good results. I must try that Sierra method...
It's important to keep in mind that "my" method is not an alternative to dither: my method and dithering have diferent goals and you can use both methods. My method simply splits the original image in 16 sections and converts each section to 16 colors. At this time (when you convert images to 16 colors) you can use dithering or not. I tested it, and I get some good results but also some bad results. Now I'm going to post here one example of a bad result when dithering:
The first two images where made using two methods of dithering (FloydSteinberg and Riemersma) and the third does not use dithering. In the two images with ditheirng, the result is a bit fuzzy and IN MY OPINION does not give any positive points, and the image without dithering is very clear. But this is only my opinion, and maybe someone can like more the results with dithering. Also, I have get other examples where dithering gives good results. Besides, dithering seems very very good if you see the image from a far distance, but this is not our case
@TheOldMan: that application for conversion would be interesting, although there are some programs that do image conversions yet. Maybe you would like to test them before starting to do that program on your own. In fact, almost every image program can convert a picture to few colors (for example, to 16 colors or 256 colors). I have used the free Ultimate Paint, and it converts to 16-color PCX well (don't forget to check the "Transparent" checkbox if you are making sprites). Also, it has another checkbox for "dither", although it doesn't have several dithering methods, it only has one). Of course ImageMagick can convert and dither too (the fragments of the images of above were converted with ImageMagick).
In case that you are still interested in making that program, well... in fact the idea that you proposed is one of the main methods to make color reduction (counting the frequency of every color). At this point, the key is choose which are the representative colors. If you search in Google for "Color reduction" you will find lots of these methods.
@GobanToba: Yes!! If there is a big part of the image where you can use only one palette, then you will have the other 15 palettes for the rest of the picture. In this case, you will probably have to do the split manually. The method that I proposed in my first post was an automatic way to do it (dividing the image in 16 square sections) but of course the results can be enhanced with your idea.